OFFSET
0,3
COMMENTS
The Turán graph T(n^2,n) is the complete n-partite graph K_{n,...,n}.
An acyclic orientation is an assignment of a direction to each edge such that no cycle in the graph is consistently oriented. Stanley showed that the number of acyclic orientations of a graph G is equal to the absolute value of the chromatic polynomial X_G(q) evaluated at q=-1.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..21
Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178.
Zhiyang Sun, Saddle-Point Asymptotics for Chromatic and Tutte Polynomial Evaluations of Complete Multipartite Graphs, arXiv:2605.04006 [math.CO], 2026.
Wikipedia, Acyclic orientation.
Wikipedia, Multipartite graph.
Wikipedia, Turán graph.
FORMULA
a(n) = A267383(n^2,n).
a(n) ~ sqrt(2*Pi) * n^(2*n^2 + 1) / exp(n^2 + n/2 - 7/24). - Vaclav Kotesovec, Feb 06 2026
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 17 2024
STATUS
approved